Question

Assuming that the concentration of Cu2+ ions in a solution is 0.25 M, the concentration of Ag+ ions in another solution is 0.50 M, and the standard reduction potential of Cu2+(aq) + 2e- → Cu(s) is +0.34 V and that of Ag+(aq) + e- → Ag(s) is +0.80 V, calculate the current density when the two solutions are separated by a salt bridge and connected by a wire.

Answer 1

To calculate the current density, we first need to find the cell potential  E_cell  of the electrochemical cell. We can use the Nernst equation to find the cell potential:E_cell = E_cell -  RT/nF  * ln Q where E_cell is the standard cell potential, R is the gas constant  8.314 J/molK , T is the temperature in Kelvin  assuming 298 K or 25C , n is the number of electrons transferred, F is the Faraday constant  96485 C/mol , and Q is the reaction quotient.First, we need to find the standard cell potential  E_cell . The standard cell potential is the difference between the standard reduction potentials of the two half-reactions:E_cell = E_cathode - E_anodeSince Ag+ has a higher reduction potential, it will act as the cathode, and Cu2+ will act as the anode:E_cell =  +0.80 V  -  +0.34 V  = +0.46 VNext, we need to find the reaction quotient  Q . For the reaction:Cu2+ aq  + 2Ag+ aq   Cu s  + 2Ag s The reaction quotient is given by:Q = [Cu2+]/[Ag+]^2Plugging in the given concentrations:Q =  0.25 M / 0.50 M ^2 = 1Now, we can plug in the values into the Nernst equation:E_cell = E_cell -  RT/nF  * ln Q E_cell = 0.46 V -   8.314 J/molK  *  298 K  /  2 * 96485 C/mol   * ln 1 Since ln 1  = 0, the second term in the equation becomes 0:E_cell = 0.46 VNow, to find the current density  j , we need to know the area  A  of the electrode and the conductivity    of the solution. However, this information is not provided in the problem. If this information were provided, we could use Ohm's law to find the current density:j =  * E_cell / A